From previous chapters, I think I have understand the twist, it is about the angular velocity and the linear velocity, the difference is that linear velocity is not one fixed point in the body but is the one in the body in coincidence with the origin instantly.
I also notice the difference Stationary/inertial reference frame
first quetion
in chapter 8.2 ,is $v_b$ the velocity of the mass center of the body? after all the inertia frame is in coincidence with the mass center instantly.
Let $r_i =(x_i, y_i, z_i)$ be the fixed location of mass $i$ in a body frame {b}, where the origin of this frame is the unique point such that $\sum_{i} m_i r_i =0$. This point is known as the center of mass.
second question
what is the relationship between eq8.22 $f_b = m(\dot v_b + [\omega_b]v_b)$ and $f_b = m(\dot v_c)$ from classical method ,$v_c$ is the linear velocity of the mass center
third question
I have read the Roy Featherstone book, the spatial acceleration is defined as $[\dot w, \ddot r - w \times \dot r]^T$ , this garantees that spatial acceleration is zero even when the body is rotating at a constant speed therefore some points are undergoing centripetal force. However in the modern robotics I find that the derivative of the twist is not accordance with the the spatial acceleration